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#### UM E-Theses Collection (澳門大學電子學位論文庫)

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Title

Monte Carlo methods in calculating value at risk

English Abstract

Almost every investor who has invested or is considering investing in a risky asset will ask what is the most lose in their portfolios. VaR (Value at Risk) gives them the exact answer. Monte Carlo methods are especially useful for studying systems with a large number of coupled degrees of freedom and VaR is a typical example. In fact, the Monte Carlo methods used in the calculation of VaR allow the construction of stochastic or probabilistic financial models as opposition to the traditional static and deterministic models, so as to enhance the treatment of uncertainty in the calculation. Based on the Monte Carlo methods to compute VaR, the approach covers market conditions ranging from the general environment considered by the existing VaR methods to the financial crises which focus on stress testing. Thus, this approach evaluates the risk more accurately and advances risk awareness of investors. This thesis reviews and summaries the calculation methods of VaR via the Monte Carlo methods. The different generations of the random numbers having normal distribution or student t distribution with correlations in computer are summarized and compared with each other in this thesis. The practical algorithms for calculating VaR are also presented, including the delta-gamma approximation with the important sampling. Copula technique is also presented and the practical algorithms for computing VaR via the Monte Carlo methods are also shown, including the Gaussian copula and the t copula. Finally, the numerical experiments for these different methods above are also given. From the comparison and conclusion, we can find different methods’ advantages and disadvantages to estimate VaR. In the first two chapters, the theories of VaR and the Monte Carlo methods are introduced, and their histories and applications in the finance field are also given, respectively. In Chapter 3, the theories of the different generations of the random numbers having normal distribution and t distribution are considered. Then the algorithms for calculating VaR via the Monte Carlo methods under those distributions are given respectively in this chapter. In Chapter 4, the theories of the generations of the random numbers using the technique of the Gaussian copula and the t copula are considered. Then the algorithms for calculating VaR via Monte Carlo methods using those copulas are given respectively in this chapter. In Chapter 5, numerical experiments for the algorithms given in Chapters 3 and 4 are shown, and the corresponding results are compared with each other by calculating these VaRs on the portfolios with different distributions or different methods, such as and the delta-gamma approximation with the important sampling.

Issue date

2010.

Author

Li, Xin

Faculty

Faculty of Science and Technology

Department

Department of Mathematics

Degree

M.Sc.

Subject

Monte Carlo method

Finance -- Mathematical models

Financial risk management

Supervisor

Ding, Deng

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Library URL
991005009579706306